Cover potatoes in cold salted water in a saucepan. Boil 10 to 15 minutes, or until tender. Drain; cool slightly before slicing in half.
Whisk together orange juice, mayonnaise, lime juice, oregano, garlic, salt, and pepper in a medium bowl; set aside.
Toss potatoes with olive oil and place cut sides down on a hot grill for 3 to 5 minutes. Once potatoes have cooled, toss with dressing and top with scallions.
A Cuban-style marinade lightens up this cookout classic.